Softmax vs Sigmoid: Which is Better?
Both Softmax and Sigmoid are activation functions used in machine learning, especially in classification tasks. They are similar in that they both squish inputs into a range of 0 to 1, but they are used in different contexts and have distinct behaviors.
1️⃣ Softmax (Multiclass Classification)
- Used for multi-class classification problems where you want to assign probabilities to each class.
- Converts raw scores (logits) into a probability distribution over multiple classes.
- The output probabilities sum to 1.
- Exponential function is applied to each input score to magnify the differences between them.
Formula:
Si=exi∑jexjS_i = \frac{e^{x_i}}{\sum_{j} e^{x_j}}Si=∑jexjexi
Where:
- xix_ixi is the raw input (logit) for class iii,
- exie^{x_i}exi is the exponential function of the logit,
- The denominator sums the exponentials of all logits to normalize the probabilities.
Use Case:
- Multiclass classification, such as identifying which of several classes (e.g., cat, dog, or bird) an image belongs to.
- Example: In neural networks, Softmax is typically used in the output layer of multi-class classification models.
Example (Python)
pythonCopy codeimport numpy as np
def softmax(x):
exp_x = np.exp(x - np.max(x)) # For numerical stability
return exp_x / np.sum(exp_x)
logits = np.array([2.0, 1.0, 0.1])
print(softmax(logits)) # Output: [0.659, 0.242, 0.099]
2️⃣ Sigmoid (Binary Classification)
- Used for binary classification problems, where the output is a probability for one class (often the “positive” class).
- Converts a single input value into a probability in the range of 0 to 1.
- Sigmoid squashes values to be between 0 and 1 but doesn’t ensure that they sum to 1 (as Softmax does).
Formula:
σ(x)=11+e−x\sigma(x) = \frac{1}{1 + e^{-x}}σ(x)=1+e−x1
Where:
- xxx is the raw input (logit).
Use Case:
- Binary classification tasks, such as predicting whether an email is spam or not, or predicting if a customer will buy a product or not.
- Example: In binary classification, Sigmoid is often used in the output layer of neural networks for predicting a probability of the positive class.
Example (Python)
pythonCopy codedef sigmoid(x):
return 1 / (1 + np.exp(-x))
logit = 0.5
print(sigmoid(logit)) # Output: 0.622
🔑 Key Differences
| Feature | Softmax | Sigmoid |
|---|---|---|
| Purpose | Multi-class classification (probabilities for each class) | Binary classification (probability for the positive class) |
| Output Range | (0, 1) but sums to 1 (probability distribution) | (0, 1) (probability for one class) |
| Input | Takes a vector of logits (scores) | Takes a single logit (score) |
| Use Case | Multi-class problems (e.g., 3 or more classes) | Binary classification (e.g., 2 classes) |
| Formula | exi∑jexj\frac{e^{x_i}}{\sum_{j} e^{x_j}}∑jexjexi | 11+e−x\frac{1}{1 + e^{-x}}1+e−x1 |
🛠️ When to Use?
- Use Softmax when dealing with multi-class classification (more than 2 classes) and you need to get a probability distribution over multiple classes.
- Use Sigmoid for binary classification (2 classes), where you’re interested in the probability of one class (often the “positive” class).
Let me know if you’d like further details! 🚀